The statements in this section merely provide background information related to the present disclosure and may not constitute prior art.
With broadband voltage/current (hereinafter “VI”) probes, such as the VI probe disclosed in U.S. Pat. No. 6,708,123, hereby incorporated by reference into the present disclosure, a calibration needs to be performed on the VI probe after its assembly. The calibration principally involves determining a linear transformation of the raw voltage and current—received from the RF sensor pickups of the VI probe—into true voltage and current measurements, from which all other relevant parameters can be derived. The transformation is depicted in equation (1) below:
                              [                                                    V                                                                    I                                              ]                =                              [                                                            a                                                  b                                                                              c                                                  d                                                      ]                    *                      [                                                                                V                    v                                                                                                                    V                    i                                                                        ]                                              Equation        ⁢                                  ⁢        1            
where [a, b; c, d], being the complex calibration coefficients for an individual frequency, and being theoretically valid for all regions in the Smith chart, are given by:
                    a        =                  -                                                                      Z                  LDT                                *                                  P                  REF                                                                                    -                                  V                                      V                    ⁢                                                                                  ⁢                    50                                                              +                                                Z                  SC                                *                                  V                                      I                    ⁢                                                                                  ⁢                    50                                                                                                          Equation        ⁢                                  ⁢        2                                b        =                                                                              Z                  LDT                                *                                  P                  REF                                                      *                          Z                              SC                ⁢                                                                                                                          -                              V                                  V                  ⁢                                                                          ⁢                  50                                                      +                                          Z                SC                            *                              V                                  I                  ⁢                                                                          ⁢                  50                                                                                        Equation        ⁢                                  ⁢        3                                c        =                                                            Z                LDT                            *                              P                REF                                                                        Z              LDT                        *                          (                                                -                                      V                                          V                      ⁢                                                                                          ⁢                      50                                                                      +                                                      Z                    OC                                    *                                      V                                          I                      ⁢                                                                                          ⁢                      50                                                                                  )                                                          Equation        ⁢                                  ⁢        4                                d        =                                                                              Z                  LDT                                *                                  P                  REF                                                      *                          Z              OC                                                          Z              LDT                        *                          (                                                -                                      V                                          V                      ⁢                                                                                          ⁢                      50                                                                      +                                                      Z                    OC                                    *                                      V                                          I                      ⁢                                                                                          ⁢                      50                                                                                  )                                                          Equation        ⁢                                  ⁢        5            
As mentioned earlier the true voltage and current are the basis for all other computations. Specifically, the impedance is derived using the four above mentioned calibration coefficients through the following formula:
                    Z        =                              V            I                    =                                                    a                *                                  V                  v                                            +                              B                *                                  V                  i                                                                                    c                *                                  V                  v                                            +                              d                *                                  V                  i                                                                                        Equation        ⁢                                  ⁢        6            
With a VI probe, some degree of inaccuracy will typically exist. This inaccuracy can be in the range of four to six percent in magnitude for impedance measurements. An internal study conducted by MKS Instruments shows that the impedance measurement error is magnified as it nears the open and short locations on the Smith chart, as illustrated in FIG. 1. Short and open calibrations also affect a VI probe's performance at high frequencies. As the frequency increases, accuracy tends to fluctuate according to some sub-sinusoidal pattern, and VI probe unit-to-unit repeatability tends to degrade at an increasing rate, as can be seen in FIGS. 2A and 2B. The degradation in accuracy and repeatability at higher frequencies can be traced back to an abnormality that occurs during calibration that can be traced by its signature in the open-calibration raw voltage and the short-calibration raw current magnitude plots, as shown in FIGS. 3 and 4. The decrease in the difference between the open, short and 50 ohm impedances can be observed in FIG. 5.
Previously, there was a limited understanding of the accuracy limitation described above. Several algorithms were implemented to address the above-described accuracy limitation with a VI probe. One solution consisted simply of measuring the impedance error vector—base-lined using a network analyzer—and modifying two of the four calibration coefficients in order to zero out the error when measuring that specific load (see equation 6). This solution, however, has consequences on the corrected frequencies in other regions of the Smith chart as can be seen in FIGS. 6 and 7. In FIGS. 6 and 7 the effects of correcting a 27 MHz signal for a near short load can be seen to negatively affect the impedance measurement performance at 50 ohms. It can also be safely assumed that the power measurements, even though only specified in a 50 ohm load, will be negatively affected, as can be deduced from the phase changes illustrated in FIG. 7. Furthermore, all other parameters measured by a VI probe will also be negatively affected besides the already discussed delivered power and impedance. These other factors include r, VSWR, forward power, reflected power and apparent power. From observing the raw calibration data, it can be easily noted that the calibration equipment performance is far from optimal into short and open load conditions. Coupled with a bad signal to noise ratio at the input of the analog to digital converters, the end result of these imperfections is a distorted, shifted, and compressed performance spread over the Smith chart.